If HKG is your first stop, for what you pay in rental, you might want to consider picking up an inexpensive GSM 900 phone there, and then getting prepaid cards in the various countries. A prepaid card in HKG from SmarTone can be purchased at many locations, including most convenience stores. They cost HK$300. Recharge vouchers come in a variety of denominations. The nice think about the SmarTone card is that it will roam in BKK (and can be refilled overseas as well... don't have to be in HKG). It also roams in China, Vietnam, Malaysia, Australia, Taiwan, and many European and south Asian countries as well. Unfortunately it doesn't roam in SIN, but you can pick up 'The M Card' for SIN$28.

Prepaid rates are generally competitive with subscriber rates.

If you feel more comfortable getting the SIMs before you leave, check out Telestial where you will of course pay a nominal surcharge for the SIMs.

If you plan to use the phone for more than just a few days you might find renting and paying the high per-minute rates to be quite expensive.